The full Moon over Bosscha
- Round
- Theory
- Points
- 20
- Level
- Bronze
- Taught in
- Section 2.8
Adapted from IOAA 2008 (Bandung), theory problem 3. We have restated it in our own words and kept the original data. The solution was last checked on 17 October 2026.
A full Moon occurred on 19 June 2008 at 00h 30m West Indonesian Time, the civil time of western Indonesia, which is UT+7 and is the mean time of the 105° E meridian. Find the shortest and the longest possible time that the Moon spends above the horizon on that night for an observer at Bosscha Observatory, at longitude 107°35′ E, latitude 6°49′ S and elevation 1300 m.
- At full Moon the Moon is opposite the Sun. On 19 June the Sun is near the June solstice, at declination +23.44° and right ascension 6h, so the Moon is near right ascension 18h. Its orbit is tilted by 5.15° to the ecliptic, so its declination is between
- The latitude is
- The Moon is above the horizon while its hour angle grows by
- The Moon moves eastward among the stars by 13.18° a day on average, so its hour angle grows by about
- Near right ascension 18h the Moon's right ascension grows faster than its longitude, by the factor
AnswerThe Moon is above the horizon for at least about 12h 45m and at most about 13h. The official solution gives 12h 18m and 12h 30m, which leave out the Moon's motion among the stars. On that night the Moon was 4.0° south of the ecliptic, at declination −27.4°, and by its computed position it rose at 17:23 on 18 June and set at 06:17 on 19 June, West Indonesian Time, so it was above the horizon for 12h 54m.
This problem also appears among the olympiad problems of Section 2.8, Problems for Chapter 2, which teaches the ideas it uses. Equation and figure numbers refer to the course.